Uniqueness for ab initio phase retrieval in macromolecular X-ray crystallography

Protein X-ray crystallography, the determination of three-dimensional structures of protein molecules from crystal X-ray diffraction data, requires determining the phases of the diffraction signal, since only the amplitude is measured. This so-called phase problem is a key component of protein X-ray crystallography. Most current methods for phasing are experimentally based and utilise either additional diffraction data from modified crystals or knowledge of the structure of a related protein. Ab initio phasing refers to computational methods that utilise only the measured diffraction amplitudes and some a priori information on protein electron densities, and potentially offer a dramatic reduction in effort over experimental methods. A key question in ab initio phasing is whether the diffraction amplitudes and the a priori information are sufficient to uniquely define the phases. The question of uniqueness is examined here for the case of a priori information on the molecular envelope.